Contribution from cross-country skiing, start time and shooting components to the overall and isolated biathlon pursuit race performance

Purpose Biathlon is an Olympic sport combining 3–5 laps of cross-country skiing with rifle shooting, alternating between the prone and standing shooting positions between laps. The individual distance and the sprint are extensively examined whereas the pursuit, with start times based on the sprint results, is unexplored. Therefore, the current study aimed to investigate the contribution from start time, cross-country skiing time, penalty time, shooting time and range time to the overall and isolated performance in biathlon World Cup pursuit races. Methods 38 and 37 stepwise linear regression analyses for each of the races were performed, including 112 and 128 unique athletes where 20 and 13 athletes had more than 20 results within top 30 during the seasons 2011/2012-2015/2016 in men and women, respectively. Results Start time (i.e. sprint race performance) together with penalty time, explained ~80% of the performance-variance (R2) in overall pursuit performance in most races (p<0.01). For isolated pursuit performance, penalty time was the most important component, explaining >54% of the performance-variance in the majority of races, followed by course time (accumulated R2 = .91-.92) and shooting time (accumulated R2 = .98-.99) (p<0.01). Approximately the same rankings of factors were found when comparing standardized coefficients and correlation coefficients of the independent variables included in the regression. Conclusion Start time (i.e. sprint race performance) is the most important component for overall pursuit performance in biathlon, whereas shooting performance followed by course time are the most important components for the isolated pursuit race performance.


Summary
The paper proposes an approach to evaluate the impact of several explanatory variables, like start and penalty time, on overall and isolated biathlon pursuit performance. The authors use stepwise linear regressions to identify the most important predictors. Furthermore, they use correlation analyses to examine the linear relationships between start time (penalty time, course time, shooting time, range time) and overall (isolated) pursuit race time behind. Particularly, they focus also on the dierences between male and female biathletes. Additionally, they describe the relationship between sprint and pursuit races.
In general, the paper discusses an interesting topic but it partially lacks of correct descriptions and applications of statistical methods. Until now, the manuscript needs to be revised because there are fundamental issues which undermine the quality of the paper severely. Furthermore, the interpretation and discussion of the results should be expanded.
2 Major Comments 1. Stepwise linear regressions: The models used to analyze the importance of the independent variables totally explain the dependent variable because there is a perfect interrelation and, thus, the dependent variable can be perfectly computed with the independent variables. For this reason, it does not seem to make sense to estimate a linear model. Generally, stepwise regression is used to make a variable selection and not necessarily to measure the variable importance. The motivation why you should use stepwise regression to identify the variable's importance should be clearer.
• If you want to compute the relative importance, you could also calculate the standardized coecients and compare them with each other.
Another approach is to use the estimators of relative importance in linear regression based on variance decomposition according to Grömping [2007]. This approach allows a comparison between dierent metrics of relative importance.
• There is no discussion about the method you used in your stepwise regression analyses. Did you use forward, backward or both selection types to choose your models?
• Moreover, there are 1200 observations per sex. You look only on the top 30 athletes in each race. This results in 40 races but you show only ndings for 38 or 37 races. Where are the other 2 respectively 3 races?
• In addition, in Table 2 you totally included 38 or 37 races to estimate the models but if you add up the number of races with best ts, you get only 34.
• The basis of each regression are 30 observations, which is a relatively small number. The interpretation of each regression result doesn't make sense because what is your general conclusion? What is the main variable which drives the general pursuit race performance? Why don't you estimate an overall model to get the relative importance of the independent variables? Denitely, it would be more dicult to get the real eects because, now, you have to consider dierent race eects, like course prole and so on but the result of this analysis would be more relevant for coaches.
• Moreover, there is no discussion about the assumption of linear regression analysis. Are they full-lled? Have you tested for heteroscedasticity or have you looked at the residuals' distribution? All in all, there are some problems in the methodical description and application. These problems should be discussed and explained in the paper to get a more reected description of the method.
2. Outliers detection: Until now, there is no consistent structure and the analyses should be revised. All outliers are removed in the stepwise regression but not in the other statistical analyses. Thus, the structure is not consistent. The means, standard deviations, condence intervals, and also the correlation analyses are biased by the outliers. For this reason, the outliers should be removed from all statistical analyses because there is no reason to include them. It would be better to use robust methods for your analyses. E.g., you could compute median, Spearman's rank correlation, a robust linear regression, and a Wilcoxon signed-rank test instead of t-test. Additionally, there are only one-dimensional outliers removed for each variable but it could also be possible that there are outliers in the two-dimensional space or multidimensional space. These outliers would also eect the statistical correlation or regression analyses. Table 2 and 4, there are 95% condence intervals estimated if there were more than 4 races that tted the regression. This does not be useful because if there are 5 observations and a 95% condence interval is calculated than only 0.25% of the observations would be outside of the interval. In principle, it cannot be assumed that a normal distribution of the parameters exists if only 5 observations are available. Moreover, the parameter distribution could be random and, thus, the distribution is not robust. Therefore, the condence intervals don't provide meaningfulness.

Correlation analyses:
The correlation analysis explanation is not adequate. There has to be a better description, why a coecient is included in the table and why not. This contributes to easier reading comprehension. Generally, the coecients should be more interpreted. E.g., the overall pursuit race time behind correlates in 6 races positively and in 3 races negatively with range time. Thus, the coecients cannot be interpreted adequately. The conclusion should be that there is no clear eect direction of range time on overall pursuit race time behind. All the other coecients are positively correlated and that is as expected. So the question arises: What can we learn from the correlation analyses?
3 Minor comments 8. Line 150-152: At this point, there is the problem that the means and also the condence intervals could be extremely eected by the total meters to climb, maximum climb, the snow conditions, and weather conditions. A explanation for the reader would be helpful.
10. Line 154-156: There should be spaces between the mean and the condence interval. In addition, place the second's symbol before the brackets (11.6 s (6.5,16.8)).